The relation (REF ) between the output field and the radiating dipole can be generally obtained in the Heisenberg picture. One typical case is that of a dipole damped by a continuum of photon modes described by an operator \(\hat{E}\)  in (REF ), in equivalence to the master equation (REF ) and in analogy to input-output theory [1]} (where \(G\)  is often related to the photon Green's function [2]}, [3]}). For example, consider superradiance in a leaky cavity, where the atoms are situated at positions where they are identically coupled to the cavity mode \(\hat{a}\)  and driven by a laser \(\Omega \) . The Hamiltonian is given by
\(\hat{H}=-\hbar \delta _a\hat{J}_z-\hbar \delta _c\hat{a}^{\dag }\hat{a}+\hbar \left[\left(g^{\ast }\hat{a}^{\dag }+\Omega ^{\ast }\right)\hat{J}+\mathrm {h.c.}\right],\) 
